3.5 Point­Slope of a Line Learning Objectives: 1. Find the equation of a line given a point and a slope. 2. Find the equation of a line given two points. 3. Build linear models using the point‐slope form of a line. 1. Find the equation of a line given a point and a slope Summary of Equations of a line Ax + By = C 1. Standard Form: 2. Slope­intercept Form: 3. y − y1 = m( x − x1 ) ; (x1 , y1 ) = given point; m = slope Point­Slope Form: y = b ; m = 0 ; (0, b ) = y‐intercept; x‐intercept = none 4. Horizontal Line: 5. Vertical Line: y = mx + b ; m = slope; (0, b ) = y‐intercept x = a ; m = undefined; (a, 0 ) = x‐intercept; y‐intercept = none Example 1. Find the equation of the line that contains the given point and has the given slope. Write the equation in slope‐intercept form, if possible. 2
1. (0, 3) ; slope = − 5
2. (4, − 8) ; slope = 2 3. 1 (− 18, − 2 ) ; slope = 4 9
4. Horizontal line that contains (3, − 1)
5. Vertical line that contains (− 2, − 7 ) 2. Find the equation of a line given two points Example 2. Find the equation of the line that contains the given points. Write the equation in slope intercept form, if possible. 1. (4, − 2 ) and (2, − 9 ) 2. (3, − 9 ) and (− 4, − 8) 3. x‐intercept = 8; y‐intercept = − 1 2